Perhaps if you draw the first and last line (the 2 extremes)...select both and go Object > Blend > Make, then select this group and acess Object > Blend > Blending Options to control the intermediate steps you can reach near the result you want.
More experimentation, using your advice:
I consider this result ideal - just a matter of making the two original shapes even more different and increasing the steps until the space between blend-generated shapes is reduced to nothing at the top - where the very first gap is seen, is where the halftone starts. Awesome. *HIGH FIVE*
With the direct selection tool (white arrow) select each anchor point of the spine curve of the blend and convert it to smooth point using the Convert to Smooth point button on the properties bar. Then move the handles of the anchor points of the spine while holding Shift to constrain vertically until you like the distribution.
Europe, Middle East and Africa